An Approximate Dual Subgradient Algorithm for Multi-Agent Non-Convex Optimization

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective,...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 58; no. 6; pp. 1534 - 1539
Main Authors Minghui Zhu, Martinez, S.
Format Journal Article
LanguageEnglish
Published IEEE 01.06.2013
Subjects
Algorithm design and analysis
Approximation algorithms
Approximation methods
Convergence
Dual subgradient algorithm
Lagrangian duality
Linear programming
Optimization
Vectors
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Summary:We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective, constraint functions, and state constraint sets are convex. In order to deal with time-varying network topologies satisfying a standard connectivity assumption, we resort to consensus algorithm techniques and the Lagrangian duality method. We slightly relax the requirement of exact consensus, and propose a distributed approximate dual subgradient algorithm to enable agents to asymptotically converge to a pair of primal-dual solutions to an approximate problem. To guarantee convergence, we assume that the Slater's condition is satisfied and the optimal solution set of the dual limit is singleton. We implement our algorithm over a source localization problem and compare the performance with existing algorithms.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2012.2228038